Abstract
We characterise the stress singularity of the OldroydB, PhanThienTanner (PTT), and Giesekus viscoelastic models in steady planar stickslip flows. For both PTT and Giesekus models in the presence of a solvent viscosity, the asymptotics show that the velocity field is Newtonian dominated near to the singularity at the join of the stick and slip surfaces. Polymer stress boundary layers are present at both the stick and slip surfaces.Byintegrating along streamlines,weverify the polymer stress behavior of r^{4/11} for PTT and r^{5/16} viscoelastic velocity field. distance from the singularity. These asymptotic results for PTT and Giesekus do not hold in the limit of vanishing quadratic stress terms for OldroydB. However, we can consider the OldroydB model in the fixed kinematics of a prescribed Newtonian velocity field. In contrast to PTT and Giesekus, this is not the correct balance for the momentum equation but does allow insight into the behavior of the OldroydB equations near the singularity. A threeregion asymptotic structure is again apparent with now a polymer stress singularity of r^{4/5}. The highWeissenberg boundary layer equations are found to manifest themselves at the stick surface and are of thickness r^{3/2}. At the slip surface, dominant balance between the upper convected stress and rateofstrain terms gives a slip boundary layer of thickness r^{2}. The solution of the slip boundary layer shows that the polymer stress is now singular along the slip surface. These results are supported through numerical integration along streamlines of the OldroydB equations in a Newtonian velocity field. The OldroydB model thus extends the point singularity at the join of the stick and slip surfaces to the whole of slip surface. As such, it does not have a physically meaningful solution in a Newtonian velocity field. We would expect a similar stress behavior for this model in the true viscoelastic velocity field.
Original language  English 

Article number  121604 
Journal  Physics of Fluids 
Volume  29 
Issue number  12 
Early online date  16 Oct 2017 
DOIs  
Publication status  Published  1 Dec 2017 
ASJC Scopus subject areas
 Condensed Matter Physics
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Jonathan Evans
 Department of Mathematical Sciences  Reader
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Institute for Mathematical Innovation (IMI)
 Centre for Nonlinear Mechanics
 EPSRC Centre for Doctoral Training in Advanced Automotive Propulsion Systems (AAPS CDT)
Person: Research & Teaching, Affiliate staff